Arithmetic & Geometric Progression

Thank you for helping!!

Q1: An arithmetic progression has n terms and common difference d, where d > 0. Prove that the difference of the sum of the last k terms and the sum of the first k terms is (n - k)kd.

Q2: Given that p = (x^2) - 2x - 1, q = (x^2) + 1, r = (x^2) + 2x -1, find all the real values of x for which

i) p, q, r are in arithmetic progression;

ii) (p^2), (q^2) and (r^2) are in geometric progression.

Q3: Given that Sn denotes the sum of the first n terms of a certain arithmetic progression in which the common difference is not zero and that S2n = kSn for all values of n, find the value of the constant k.

Thank you very very much!